I've done some further research and, as suspected, the Sony Assistant was completely wrong. I managed to locate the user manual for the turntable which confirmed headphones could be connected.
I resolved the issue by following the procedure in the manual for deleting all previous bluetooth connections (holding the pairing button on the turntable for a period of time - 6 seconds I think). After this, both my Sony earbuds and Bose over-ear headphones both paired.
